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Physics of Music, Lecture 7, D. Kirkby2 Miscellaneous Homework #3 is due on Thursday. There will be no new homework assigned on Thursday. The midterm will be held in class Thursday Oct 31 and will cover the material in Lectures 1-8 and Homework 1-3. We will have a review session during class this coming Thursday (Oct 24). The final exam is scheduled for Friday Dec 13 from 10:30am-12:30pm. Conflicts with present office hours? (Wed 9-11am). Replace 9-10am with 12-1? 1-2? 3-4?

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Physics of Music, Lecture 7, D. Kirkby3 Review of Lecture 6 In this unit, we are exploring the relationship between the physical and psychological attributes of musical sound. We took a tour of the human ear by following a sound wave on its path from the pinnae through to the signals sent to the brain on the auditory nerve.

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Physics of Music, Lecture 7, D. Kirkby4 Our hearing capabilities are primarily determined by the mechanical response of the basilar membrane in the cochlea. The basilar membrane sends signals to the brain that encode where it vibrates (ie, the sound’s wavelength) and the rate at which it vibrates (ie, the sound’s frequency). These two pieces of information are normally redundant.

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Physics of Music, Lecture 7, D. Kirkby5 The Limits of Hearing The conventional wisdom is that our hearing covers the range from 20-20,000 Hz. In fact, most people’s hearing covers a smaller range. A quiet sound is harder to hear than a loud sound of the same frequency. Therefore a description of hearing range must specify the sound intensity as well as its frequency.

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Physics of Music, Lecture 7, D. Kirkby6 We are most sensitive to sounds in the range 2000-5000 Hz where the ear canal acts as a resonator. Speech relies on a relatively small range of frequencies and intensities. Music places greater demands on our hearing. Frequency (Hz) Source: “The Science of Sound”, Fig 5.1, Rossing, Moore & Wheeler, 3rd ed.

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Physics of Music, Lecture 7, D. Kirkby8 Demonstration of Effects of Hearing Loss Hearing range also decreases after long-term exposure to background noise. This loss is usually most pronounced at intermediate frequencies in the range 2000-8000 Hz. For more information, refer to Chapters 30-31 of your textbook.

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Physics of Music, Lecture 7, D. Kirkby9 Infrasound Sounds below the threshold of human hearing are called infrasounds. At low intensities, infrasound has potential for long-range communication and atmospheric monitoring (in particular, detecting nuclear tests). At high intensities, infrasound can cause dizziness and nausea (primarily via the semicircular canals of your inner ears) and even internal bleeding due to internal organs rubbing against each other. CTBT IMS network

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Physics of Music, Lecture 7, D. Kirkby11 Hearing Range of Animals Animals have a wide range of hearing capabilities. Elephants are particularly sensitive to infrasound. Mice are particularly sensitive to ultrasound, but so are whales! http://shop.store.yahoo.com/animalmedicstore/sildogtrainw.html See also: http://www.lsu.edu/deafness/HearingRange.htmlhttp://www.lsu.edu/deafness/HearingRange.html

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Physics of Music, Lecture 7, D. Kirkby12 What is Your Range of Hearing? Listen to these pure SHM tones of different frequencies. How low a sound can you hear? How high a sound? This demonstration needs a big speaker: why? (We will cover some of the issues of speaker design in Lecture 16.) The lowest note on a piano has a frequency of about 27 Hz but is easily audible. Is this consistent with the results of the test you just did?

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Physics of Music, Lecture 7, D. Kirkby13 Critical Bands The basilar membrane in the cochlea responds to a pure (SHM) sound by vibrating at a position along its length that depends on the sound’s wavelength: 400 Hz 4000 Hz

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Physics of Music, Lecture 7, D. Kirkby14 Even for a sound of a single wavelength, the vibrations of the basilar membrane are spread out over a length of about 1.3 mm (compared with the total membrane length of 30mm). Therefore, two sounds of slightly different wavelengths will result in overlapping vibrations (and therefore overlapping signals to the brain). The correspond range of frequencies (band) is called a critical band.

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Physics of Music, Lecture 7, D. Kirkby15 Two pure sounds are harder to distinguish when their frequencies lie within the critical band since the brain must disentangle their overlapping signals. Source: “The Science of Sound”, Fig 5.9, Rossing, Moore & Wheeler, 3rd ed. Position along Basilar membrane

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Physics of Music, Lecture 7, D. Kirkby16 The human range of hearing is divided into about 24 critical bands (but the bands do not have fixed boundaries). The size of the critical band is about 100 Hz at low frequency and then increases in proportion with frequency at higher frequencies. We will revisit critical bands several times in this unit… Source: “The Science of Sound”, Fig 5.10, Rossing, Moore & Wheeler, 3rd ed.

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Physics of Music, Lecture 7, D. Kirkby17 Critical Bands and Harmonics The first six harmonics of C 3 (128 Hz) are well separated, but higher harmonics are more difficult to distinguish. Source: Campbell, M. and Greated, C. (1987). The Musician's Guide to Acoustics. New York: Shirmer Books. As a result, we can expect that high harmonics contribute less to our subjective impression of a complex musical sound than the lower (1-6) harmonics.

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Physics of Music, Lecture 7, D. Kirkby18 Binaural Hearing We receive signals from two ears. How do these signals differ when listening to a single pure sound? Listen to this SHM tone with your eyes closed, and try to determine its source.

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Physics of Music, Lecture 7, D. Kirkby19 Most people can locate a sound’s source with an accuracy of 1-10 degrees (1 degree is about the width of your thumb when held at arm’s length). This ability is primarily based on two cues: Timing differences Intensity differences Source: “The Science of Sound”, Fig 5.11, Rossing, Moore & Wheeler, 3rd ed.

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Physics of Music, Lecture 7, D. Kirkby20 Timing Differences Between Each Ear Your head is about 20cm wide, so sound arriving from the side takes about 600 microseconds ( = 0.6 msec) longer to reach your far ear than your near ear. The direct sound arriving from a source located directly in front, above, or behind you reaches both ears at the same time. Your brain can detect timing differences as small as 30 microseconds between the signals from each ear. Source: Mills, "Auditory Localization", in Tobias, ed., Foundations of Modem Auditory Theory, Academic Press, 1972

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Physics of Music, Lecture 7, D. Kirkby21 Role of Reflections in Localization The signals received by each are more complicated that we would predict based only on the different distances to the source of the sound. Multiple reflections from the folds of the pinnae play an important role in shaping the sound heard from different directions, and provide additional cues to the brain. Only sounds arriving from slightly behind you can enter your ear canal directly. Sounds are delayed by reflections the more the source is in front of your. Sounds arriving from below are also delayed relative to those arriving from above. For more info see http://www.sfu.ca/sonic-studio/handbook/Binaural_Hearing.htmlhttp://www.sfu.ca/sonic-studio/handbook/Binaural_Hearing.html

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Physics of Music, Lecture 7, D. Kirkby22 Intensity Differences Between Each Ear Timing differences provide the main cue for localizing pure sounds with frequencies below about 1500 Hz. For localizing higher frequency sounds, the attenuation of the sound heard by the far ear is the main cue. Your head shadows high frequency sounds more than low frequency sounds because it absorbs high frequencies more and they diffract less. Source: “The Science of Sound”, Fig 5.11, Rossing, Moore & Wheeler, 3rd ed.

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Physics of Music, Lecture 7, D. Kirkby23 Head Tracking of Sound Sources The brain receives complex signals that encode several cues with information about the location of a sound source. However, making sense of all this information is not easy! One of the most powerful strategies is to turn your head and see how the timing and intensity of the sound changes. Even with your eyes closed, you instinctively turn to face a localized source of sound.

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Physics of Music, Lecture 7, D. Kirkby24 Localization and Headphones Delivering a sound through headphones defeats most of our mechanisms for localizing the sound’s source. Sounds all enter the ear at the same angle so there is no variation in the reflections from the pinnae. The timing and intensity can be different for each ear, but turning your head does not vary these parameters. How would you record & playback sounds to improve upon these limitations of traditional headphones?

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Physics of Music, Lecture 7, D. Kirkby26 Pure Waves of Sound and Light A pure sound wave is the result of a Simple Harmonic Motion and has a definite unique frequency. Most musical sounds are not pure, but are combinations of many sounds. (colors are approximate!) A pure light wave corresponds to a spectral color, ie, one produced by a prism or visible in a rainbow. Most colors (brown, pink, …) are not pure, but are combinations of spectral colors (more on this in the next Lecture).

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Physics of Music, Lecture 7, D. Kirkby27 Frequency Ranges of Hearing and Vision You can hear pure sounds over a frequency range of almost 20-20,000 Hz. This corresponds to about 9 octaves of dynamic range. You can see pure colors over a frequency range of about 400-700 GHz. This corresponds to just under one octave! Middle C 256 Hz 32 Hz 16384 Hz hearing range vision range

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Physics of Music, Lecture 7, D. Kirkby28 Physical Ingredients to Perceived Loudness We can characterize the quantity of sound at each stage: Sound = Production + Propagation ( + Detection) The quantity of sound produced by a source is measured by its total power output level (usually given in Watts). The quantity of sound propagating through the air at some point is measured by the amplitude of the pressure disturbance (usually given in N/m 2 ). The quantity of sound reaching a detector is measured as the power reaching a unit area (usually given in W/m 2 ).

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Physics of Music, Lecture 7, D. Kirkby29 These three physical measures of the quantity of sound produced are all related. For example, the detected sound intensity at a distance R from a spherical source source of total power W is given by: I = W / (4  R 2 ) The detected intensity varies as the square of the pressure level: I = (p/20) 2 (p in N/m 2, I in W/m 2 )

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Physics of Music, Lecture 7, D. Kirkby30 Combining these two relationships, we find that for a spherical source the sound pressure level drops off as 1/R with distance R from the source. Try this demo in which speech is recorded 25, 50, 100, and 200 cm from a microphone: The resulting sound pressure levels reaching your ear should (ideally) decrease by 1/2 each time and the intensity levels should decrease by 1/4 each time. (What effects might spoil this expected ideal behavior?) How did your subjective impression of the loudness change with each step away from the microphone? Would you describe the decrease as more like 1/2 or 1/4? Source: Auditory Demonstrations, #4, Houtsma, Rossing, Wagenaars (IPO-NIU/ASA)

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Physics of Music, Lecture 7, D. Kirkby31 Perception of Loudness for Pure Tones The perceived loudness of a pure tone depends primarily on the amplitude of the pressure disturbance that it creates as it travels through air. The contours in this plot show the pressure levels that are (on average) perceived to have equal loudness, for different frequencies. sound pressure level (logarithmic scale)

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Physics of Music, Lecture 7, D. Kirkby32 What is Your Loudness Threshold? Low-frequency sounds appear quieter than high-frequency sounds of the same intensity. Try this demonstration to hear this for yourself. First calibrate the volume so that this 1000 Hz test signal is barely audible: Next, listen to these 14 sets of repeated tones getting progressively quieter, and count how many steps you can hear: Source: Auditory Demonstrations, #6, Houtsma, Rossing, Wagenaars (IPO-NIU/ASA) Source: Auditory Demonstrations, #6, Houtsma, Rossing, Wagenaars (IPO-NIU/ASA)

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Physics of Music, Lecture 7, D. Kirkby33 Each tone is repeated 10 times with the intensity detected by your ear dropping by about 1/3 each time (-5 phons). The tones are at frequencies of 125, 250, 500, 1000, 2000, 4000, 8000 Hz. sound pressure level (logarithmic scale)

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Physics of Music, Lecture 7, D. Kirkby34 We are most sensitive to sounds in the 3000-5000 Hz range where the ear canal responds resonantly. The threshold of audibility is at a detected sound intensity of about 10 -12 W/m 2 and the threshold of pain is at an intensity of about 1 W/m 2. This is a huge dynamic range of 1:1,000,000,000,000 !

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Physics of Music, Lecture 7, D. Kirkby35 Degrees of Loudness in Music Written music often includes directions for how loud notes should be played (“dynamics”). These directions are usually based on a scale of 6 different degrees of loudness: pp, p, mp, mf, f, ff. The range of sound intensities (loudest/quietest) that orchestral instruments are typically capable of ranges from as little as 3x (English horn) up to almost 100x (French horn). However, most people need a range of at least 10x in order to identify six distinct loudness levels. Therefore six degrees of musical dynamics are wishful thinking for some instruments!

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Physics of Music, Lecture 7, D. Kirkby36 Perceived Loudness and Sound Duration How does the perception of the loudness of a sound depend on how long it lasts? Listen to this demonstration of sounds of decreasing intensity in 7 groups of decreasing duration: This example uses noise rather than pure tones. Successive bursts of noise decrease in intensity in 8 steps. The duration of the bursts decreases after each group of 8: 1000, 300, 100, 30, 10, 3, 1 ms. Source: Auditory Demonstrations, #8, Houtsma, Rossing, Wagenaars (IPO-NIU/ASA)

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Physics of Music, Lecture 7, D. Kirkby37 Experiments like these have shown that your brain measures the loudness of a sound during an interval of about 200 ms (1/5 of a second). This means that sounds of equal intensity lasting 200 ms or longer have the same perceived loudness, but shorter sounds appear quieter. 200ms This extra silence is averaged with the short burst to give the impression of a quieter sound. Sound intensity Time

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Physics of Music, Lecture 7, D. Kirkby38 Summary Whether a sound is audible or not depends mostly on its intensity and frequency. Critical bands measure the size of the region of your basilar membrane that vibrates in response to a pure tone. The primary purpose of binaural hearing is to localize the source of a sound. Variations in timing (low frequency) and intensity (high frequency) are the main cues. The perceived loudness of a pure tone depends mainly on the sound pressure level, but is also affected by the sound frequency and duration.

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Physics of Music, Lecture 7, D. Kirkby39 Review Questions What role does the response of your Basilar membrane play in your ability to distinguish pure tones of slightly different frequencies? How do your senses of hearing and vision compare? We saw that hearing has a much larger dynamic range. In what ways does vision exceed the capabilities of hearing? How much quieter does a sound appear when you move twice as far from its source? Why can you easily hear the lowest note on the piano (with a fundamental frequency of 27 Hz) but cannot hear a pure tone with the same frequency?